1. Field of the Invention
This invention pertains to an unmanned nonholonomic wheeled robot vehicle that automatically drives on a flat or moderately tilted ground. More specifically, this invention claims a method of how to control unmanned vehicles smoothly when given a geometrical path specification, which is a sequence of directed straight lines and circles described in the global coordinate system.
2. Description of the Related Art
Unmanned robot vehicles have been used for the automatic material transfer and/or handling purposes in factories, in hospitals, and in clean rooms for semiconductor manufacturing. In order to navigate the unmanned vehicles, the most widely used method is to attach inductive wires or optical reflexive tapes on the floor to tell the vehicle whether it is on track.
However, these conventional methods entails three barriers that limit more extensive applications of unmanned vehicles: The inductive wires and optical tapes are subject to wear because vehicles and people could step on them; Modifying and creating their path patterns is time consuming and expensive; In environments such as in semiconductor factories, even the use of wires and tapes should be avoided, because they are potential source of dusts.
The theoretical aspect of path-tracking for nonholonomic wheeled mobile robots by feedback controllers has been studied from various points of view. Motion planning/control problems for autonomous vehicles is one of the most difficult problems in robotics, because these motions are under nonholonomic constraints and the equations are not integrable. See Goldsteing, H., Classical Mechanics, Second Edition, Addison-Wesley, pp. 11-16, 1980 and Laumond, J. P., "Feasible Trajectories for Mobil Robots with Kinematic and Environment Constraints," in Intelligent Autonomous Systems, (O. L. Hertzberger and F. C. A. Groen, eds), pp. 346-354, 1987. The "configuration tracking" problem, when posed as stabilizing a nonholonomic vehicle to a given final configuration is known to have no smooth-state feedback solution, as described in Brockett, R. W., "Asymptotic Stability and Feedback Stabilization," in Progress in Math., vol. 27, Birkhauser, pp. 181-208, 1983. To overcome this difficulty, Samson and Pomet proposed a smooth time varying feedback control law for stabilizing a robot, or even a chained system of wheeled robots to a given final configuration. See: Samson, C. "Velocity and Torque Feedback Control of a Nonholonomic Cart," in Advanced Robot Control, Lecture Notes in Control and Information Sciences, No. 162, pp. 125-151, 1991, Samson, C., "Time-varying Feedback Stabilization of Car-like Wheeled Mobil Robots," International Journal of Robotics Research, vol. 12, No. 1, pp. 55-64, 1995, and Pomet, J. B., "Explicit Design of Time Varying Stabilizing Feedback Laws for a Class of Controllable Systems without Drift," System and Control Letters, vol. 18, pp. 139-145, 1992. Others such as Canudas and S.o slashed.rdalen have proposed piecewise smooth feedback laws for exponentially stabilizing a mobile robot. See: Canudas de Witt, C. and S.o slashed.rdalen, O. J., "Exponential Stabilization of Mobil Robots with Nonholonomic Constraints," IEEE Transaction on Automatic Control, Vol 37, pp. 1791-1797, 1992. For the specific problem of tracking a simple path such as a straight-line or a circle, DeSantis has developed a control rule based on the geometric path tracking principle for a tractor-trailer-like robots to track a straight line or a circular arc. See: DeSantis, R. M., "Path-tracking for a Trailer-like Robot," International Journal of Robotics Research, Vol. 13, No. 6, pp. 533-543, 1994. Murray and Sastry use sinusoidal input to solve a similar nonholonomic motion planning problem. See Murray, R. M., and Sastry, S. S., "Steering Nonholonomic Control Systems Using Sinusoids," in Nonholonomic Planning, Li and Canny eds., Kluwer Academic Publishers, pp. 23-51. 1993.
The research article, "A Stable Tracking Control Method for an Autonomous Mobile Robot," by Kanayama, et al., in Proc. IEEE International Conference on Robotics and Automation in Cincinnati, Ohio, pp. 384-389, May 1990, by this inventor is the closest prior technology to solve the path tracking problem for autonomous vehicles. Given a moving reference target, this method computes a pair (.upsilon., .OMEGA.) of the goal linear velocity .upsilon. and the goal rotational velocity .OMEGA. knowing the vehicle's own current state. A reference state is (p.sub.r, .theta..sub.r, .upsilon..sub.r, .OMEGA..sub.r) that the vehicle should follow, where p.sub.r is the reference point, .theta..sub.r the reference orientation, .upsilon..sub.r the reference linear speed, and .OMEGA..sub.r the reference rotational speed. Since the curvature .kappa. is equal to .OMEGA./.upsilon., this method can be said to be evaluating the target speed and curvature among other control variables. This method has the following shortcomings as a solution to the aforementioned problem:
(1) This method is proven effective in tracking straight lines only. The fact that this method is optimal for tracking circles or a more complex path cannot be proved. PA1 (2) The vehicle guidance method of using the moving reference state imposes an unnecessary constraint on its movement in the heading. PA1 (3) This method is computing curvature .kappa. itself instead of its derivative ##EQU1## Therefore, if there is a discontinuous change in the reference state, its curvature may have a discontinuity which may give a shock to the vehicle or may cause slippage in its motion.
While the above theoretical approaches are mathematically elegant and general enough to be applied to a variety of situations, these procedures have not yielded the simplest and most efficient feedback controllers for the specific problem of "line/circle tracking". The aforementioned tracking-control method is not satisfactory to this motion control problem either. To solve this shortcoming this invention addresses another solution to how to control a nonholonomic vehicle to track a path consisting of directed straight lines and directed circular arcs. This invention discloses a new solution using the "steering function" and a "neutral switching principle", which are simple and appropriate for real-time applications. Since this invention realizes continuous curvature motion, slippage of wheels on the ground can be minimized.